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logbin (version 1.2)

logbin.allref: Parameterisation for CEM Algorithm

Description

A workhorse function for logbin, logbin.allref takes the formula and data for a log-link binomial GLM and produces a list of all parameterisations needed for the associated CEM algorithm.

Usage

logbin.allref(object, data = environment(object), mono, start = NULL)

Arguments

object
a model formula or a terms object for the logbin model.
data
a data frame created with model.frame. If another sort of object, model.frame is called first.
mono
a vector indicating which terms should be restricted to have a monotonically non-decreasing relationship with the outcome.
start
starting values for the parameters in the linear predictor.

Value

A list with components:
allref
a named list, with one component for each term in the model. Each component is itself a list, whose components are each of the parameterisations for that term.If start was specified, the first component for each term will correspond to the parameterisation specified by start.
terms
the terms component of object.
data
the object passed into the data argument, or the result of calling model.frame with data.
monotonic
a named logical vector indicating which components of terms are restricted to be monotonically non-decreasing.
start.new
a reparameterised version of start, corresponding to the first parameterisation in allref. NULL if start was not supplied.

Details

In the CEM algorithms employed by logbin, the parameter space is partitioned into a collection of restricted parameter spaces (see Marschner, 2014). logbin.allref finds the list of possible parameterisations of each term in the model.

If a term x has a TRUE value for is.factor(x), is.character(x) or is.logical(x), it is considered to be a categorical covariate. This has a parameterisation for each level of the factor.

Otherwise the covariate is considered to be continuous, in which case it has two possible parameterisations, relating to the minimum and maximum observed values.

If a covariate is restricted to be monotonic via the mono argument, it has only one parameterisation.

logbin considers all possible combinations of the parameterisations of each covariate, and for each calls logbin.design to create the appropriate non-negative design matrix to be used in the EM algorithm.

References

Marschner, I. C. (2014). Combinatorial EM algorithms. Statistics and Computing 24(6): 921--940.

Marschner, I. C. and A. C. Gillett (2012). Relative risk regression: reliable and flexible methods for log-binomial models. Biostatistics 13(1): 179--192.

See Also

logbin